Does it power on at all, or just no sound? If the former, check the fuse, if the latter it could well be the protection circuits which may prove expensive to put right. My LMII suffered a slight drop (only a foot or so) but in a Markbass padded bag whilst unloading for a short gig. 5 songs in (and luckily the last of the set) and my sound cut out. Blue power light was on, clipped light flickered as it should but no sound. Turned it off and on again and sound back for about a second. I swapped speaker leads and same thing. Ended up having to go direct in to the PA to finish the set. (FYI, I was using a MB 1x12 cab too, so not an impedance mis-match).
Couple of days later I tried it at home at relatively low volume for about 3 hours and it was fine. So I put it down to dirty power at the venue tripping the poweramp's protection circuit.
Fast forward a week or so to a band rehearsal. Used the head with a rented cab in the studio and after about 45 mins it cur out again. Turned it off for a minute or two, tried it again and I got about another 15 mins out of it. I knew it was a sick amp.
Took it into a local amp repairers and they confirmed it was the protection circuits kicking in, but due to the nature of the amp and the surface mounted PCB, it would be an enormous task to find the exact fault, and replacing the entire main board, components and all would be faster and cheaper. However, being a discontinued model they had to get on to the distributor to get a refurb board.
I'm sorry to say that it cost me just over £200 to get it fixed and up and running again. So just to warn you that it could be expensive if it's a damaged board. You might be lucky though as the LMIII is a current model, so parts should be easier to obtain. You might even be covered by warranty if it's not that old.